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#27303012

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 121 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(55,57)(58,61)(59,67)(60,73)(62,87)(63,83)(64,82)(65,84)(66,92)(68,102)(69,99)(70,98)(71,100)(72,105)(74,112)(75,110)(76,79)(77,111)(78,85)(80,88)(81,89)(86,109)(90,118)(91,117)(93,116)(94,96)(95,120)(97,103)(101,114)(104,115)(106,119)(107,121)(108,113);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,60,65,77)(59,66,71,95)(61,79,84,110)(62,86,90,113)(63,76,64,75)(67,96,100,116)(68,101,104,106)(69,94,70,93)(72,103,107,85)(73,83,111,82)(74,88,91,89)(78,114,97,119)(80,108,81,109)(87,117,118,112)(92,99,120,98)(102,121,115,105);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(58,59,65,71)(60,72,77,107)(61,78,84,97)(62,85,90,103)(63,70,64,69)(66,91,95,74)(67,80,100,81)(68,88,104,89)(73,92,111,120)(75,101,76,106)(79,116,110,96)(82,102,83,115)(86,93,113,94)(87,98,118,99)(105,108,121,109)(112,114,117,119)

Polycyclic presentation:

2^8,53|a^2=h,b^2=h,d^2=gh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^52,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,i^b=i^52,d^c=dgh,e^c=eg,f^c=fh,g^c=gh

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 88488);